Which of the following numbers is a multiple of 4? ${46,56,66,85,86}$
Answer: The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $46 \div 4 = 11\text{ R }2$ $56 \div 4 = 14$ $66 \div 4 = 16\text{ R }2$ $85 \div 4 = 21\text{ R }1$ $86 \div 4 = 21\text{ R }2$ The only answer choice that leaves no remainder after the division is $56$ $ 14$ $4$ $56$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $56$ $56 = 2\times2\times2\times7 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $56$. We can say that $56$ is divisible by $4$.